Problem: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{z^2 + 5z}{z^2 - z - 30}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{z^2 + 5z}{z^2 - z - 30} = \dfrac{(z)(z + 5)}{(z - 6)(z + 5)} $ Notice that the term $(z + 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(z + 5)$ gives: $p = \dfrac{z}{z - 6}$ Since we divided by $(z + 5)$, $z \neq -5$. $p = \dfrac{z}{z - 6}; \space z \neq -5$